Abstract
The barrier and penalty function methods for solving mathematical programming problems have been widely used for both theoretical and computational purposes. In a penalty approach, any point outside of the feasible region is assigned a penalty while, in a barrier approach, those feasible solutions near the boundary of the feasible region are subject to a penalty. Both approaches are designed to prevent the search process for an optimal solution from wondering away from the feasible region. They can be considered as an objective-perturbation approach. This chapter studies the objective-perturbation approach by using the entropic function, \(\sum {_j x_j \ln x_j } \) for solving four classes of problems, namely, linear programming problems in Karmarkar’s form, linear programming programs in standard form, convex quadratic programming problems, and linear and convex quadratic semi-infinite programming problems.
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Fang, SC., Rajasekera, J.R., Tsao, HS.J. (1997). Entropic Perturbation Approach to Mathematical Programming. In: Entropy Optimization and Mathematical Programming. International Series in Operations Research & Management Science, vol 8. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-6131-6_5
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DOI: https://doi.org/10.1007/978-1-4615-6131-6_5
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